Understanding the Concepts

* Acceleration due to gravity (g): This is the constant acceleration experienced by objects falling freely near the Earth's surface. It's approximately 9.8 m/s². This means the object's velocity increases by 9.8 meters per second every second.

* Initial velocity (v₀): Since the ball is dropped, its initial velocity is 0 m/s.

* Final velocity (v): This is the velocity the ball reaches, which is 22.8 m/s.

Formula

We can use the following formula to relate acceleration, initial velocity, final velocity, and time:

v = v₀ + at

where:

* v = final velocity

* v₀ = initial velocity

* a = acceleration

* t = time

Solving for Time

1. Plug in the known values:

* v = 22.8 m/s

* v₀ = 0 m/s

* a = 9.8 m/s²

The equation becomes: 22.8 = 0 + (9.8)t

2. Solve for t:

* 22.8 = 9.8t

* t = 22.8 / 9.8

* t ≈ 2.33 seconds

Answer

It will take approximately 2.33 seconds for the ball to reach a speed of 22.8 m/s.